Skip to main content
SpringerLink
Log in

GRASP with Path-Relinking for Facility Layout

  • Conference paper
Models, Algorithms, and Technologies for Network Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 59))

Abstract

This paper proposes a mathematical formulation for the facility layout problem (FLP) based on the generalized quadratic assignment problem (GQAP). The GQAP is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. As a case study, we adapt the GRASP with path-relinking (GRASP-PR) heuristic introduced in Mateus et al. (J. Heuristics 17:527–565, 2011) for the hospital layout problem (HLP). In the HLP, we are given a set of areas in a hospital where medical facilities, such as surgery and recovery rooms, can be located and a set of medical facilities, each facility with a required area, that must be located in the hospital. Furthermore, we are given a matrix specifying, for each ordered pair of facilities, the number of patients that transition from the first to the second facility. The objective of the assignment is to minimize the total distance traveled by the patients. We illustrate our algorithm with a numerical example.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bazaraa, M.S.: Computerized layout design: a branch and bound approach. AIIE Trans. 7(4), 432–438 (1975)

    Article  MathSciNet  Google Scholar 

  2. Feo, T.A., Resende, M.G.C.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Foulds, L.R., Robinson, D.F.: A strategy for solving the plant layout problem. Oper. Res. Q. 27(4), 845–855 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  5. Glover, F.: Tabu search and adaptive memory programing—advances, applications and challenges. In: Barr, R.S., Helgason, R.V., Kennington, J.L. (eds.) Interfaces in Computer Science and Operations Research, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 1–75. Kluwer Academic, Dordrecht (1996)

    Google Scholar 

  6. Kaufman, L., Broeckx, F.: An algorithm for the quadratic assignment problem using Bender’s decomposition. Eur. J. Oper. Res. 2(3), 207–211 (1978)

    Article  MATH  Google Scholar 

  7. Koopmans, T.C., Beckmann, M.: Assignment problems and the location of economic activities. Econometrica 25(1), 53–76 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kusiak, A., Heragu, S.S.: The facility layout problem. Eur. J. Oper. Res. 29(3), 229–251 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  9. Laguna, M., Marti, R.: GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS J. Comput. 11, 44–52 (1999)

    Article  MATH  Google Scholar 

  10. Lawler, E.L.: The quadratic assignment problem. Manag. Sci. 9(4), 586–599 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mateus, G.R., Resende, M.G.C., Silva, R.M.A.: GRASP with path-relinking for the generalized quadratic assignment problem. J. Heuristics 17, 527–565 (2011)

    Article  MATH  Google Scholar 

  12. Resende, M.G.C., Ribeiro, C.C.: GRASP with path-relinking: recent advances and applications. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Metaheuristics: Progress as Real Problem Solvers, pp. 29–63. Springer, Berlin (2005)

    Chapter  Google Scholar 

  13. Resende, M.G.C., Ribeiro, C.C.: Greedy randomized adaptive search procedures: advances and applications. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, 2nd edn., pp. 293–319. Springer, Berlin (2010)

    Google Scholar 

  14. Ribeiro, C.C., Resende, M.G.C.: Path-relinking intensification methods for stochastic local search algorithms. J. Heuristics 18, 193–214 (2012)

    Article  Google Scholar 

  15. Rosenblatt, M.J.: The facilities layout problem: a multigoal approach. J. Prod. Res. 17 (1979)

    Google Scholar 

Download references

Acknowledgements

The research of R.M.A Silva was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq), the Foundation for Support of Research of the State of Minas Gerais, Brazil (FAPEMIG), Coordination for the Improvement of Higher Education Personnel, Brazil (CAPES), Foundation for the Support of Development of the Federal University of Pernambuco, Brazil (FADE), the Office for Research and Graduate Studies of the Federal University of Pernambuco (PROPESQ), and the Foundation for Support of Science and Technology of the State of Pernambuco (FACEPE).

Author information

Authors and Affiliations

  1. Centro de Informática, Federal University of Pernambuco, Av. Jornalista Anibal Fernandes, s/n—Cidade Universitária, CEP 50740-560, Recife, PE, Brazil

    R. M. A. Silva

  2. Algorithms and Optimization Research Department, AT&T Labs Research, 180 Park Avenue, Room C241, Florham Park, NJ, 07932, USA

    M. G. C. Resende

  3. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL, 32611, USA

    P. M. Pardalos

  4. Dept. of Computer Science, Federal University of Minas Gerais, CEP 31270-010, Belo Horizonte, MG, Brazil

    G. R. Mateus

  5. Departamento de Engenharia de Minas e de Petróleo, Escola Politécnica da Universidade de São Paulo, Av. Prof. Mello Moraes, 2373, Butantã, CEP 05508-030, São Paulo, SP, Brazil

    G. De Tomi

Authors
  1. R. M. A. Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. G. C. Resende
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. M. Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. R. Mateus
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. De Tomi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. M. A. Silva .

Editor information

Editors and Affiliations

  1. Dept. of Industrial and Systems Engineer, University of Florida, Gainesville, Florida, USA

    Boris I. Goldengorin

  2. Department of Applied Mathematics, National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A. Kalyagin

  3. Department of Industrial & Systems Engin, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this paper

Cite this paper

Silva, R.M.A., Resende, M.G.C., Pardalos, P.M., Mateus, G.R., De Tomi, G. (2013). GRASP with Path-Relinking for Facility Layout. In: Goldengorin, B., Kalyagin, V., Pardalos, P. (eds) Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8588-9_11

Download citation

Publish with us

Policies and ethics

Search

Navigation